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Research Article

Acoustic and Thermodynamic Properties of Binary Liquid Mixtures of Acetophenone and Benzene

K. Saravanakumar, R. Baskaran and T.R. Kubendran
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Densities and ultrasonic velocity of binary mixtures of acetophenone with benzene at 303.15, 313.15 and 323.15 K were measured over the entire composition range. From these experimental data, the internal pressure (πi), free volume (Vf), Gibb’s free energy (GE), viscous relaxation time (τ) were calculated. Also, the excess internal pressure (πi) and ultrasonic velocity (UE) and excess free volume were calculated. Ultrasonic velocities theoretically evaluated using Nomoto’s relation, Rao’s specific sound velocity relation and Junjie’s equation are compared with experimental values to check applicability of these equations to the systems studied. The relative merits of these theories and relations were discussed.

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  How to cite this article:

K. Saravanakumar, R. Baskaran and T.R. Kubendran, 2010. Acoustic and Thermodynamic Properties of Binary Liquid Mixtures of Acetophenone and Benzene. Journal of Applied Sciences, 10: 1616-1621.

DOI: 10.3923/jas.2010.1616.1621

Received: December 06, 2009; Accepted: April 15, 2010; Published: June 26, 2010


Ultrasonic velocity of sound waves in a medium is fundamentally related to the binding forces between the molecules. Ultrasonic velocities of the liquid mixtures consisting of polar and non-polar (Mehra and Pancholi, 2007) components are of considerable importance in understanding intermolecular interaction between component molecules and find applications in several industrial and technological processes (Pal and Kumar, 2004; Rao et al., 2005). Ultrasonic velocity measurements have been employed extensively to detect and assess weak and strong molecular interactions in binary mixtures, because mixed solvents find practical applications in many chemical and industrial processes. Increasing use of benzene and acetophenone in many industrial processes have greatly stimulated the need for extensive information on the acoustic and transport properties of these liquids and their mixtures. The parameters such as ultrasonic velocity (u), density (ρ) and derived parameters such as internal pressure (πi), free volume (Vf) viscous relaxation time (τ) provide better insight into intermolecular interactions. The investigation is carried out to study of molecular interactions in the binary liquid mixtures of acetophenone-benzene. Several researchers (Savaroglu and Aral, 2004; Sundharam and Palaniappan, 2005) carried out ultrasonic investigations on liquid mixtures and correlated the experimental results of ultrasonic velocity with the theoretical relations of Nomoto, Vandeal and Vangeel and Rao’s specific velocity and interpreted the results in terms of molecular interactions. The sound velocity in binary liquid mixtures from various theoretical models has been compared in the present paper. An attempt has been made to compare the merits of the existing relations in binary liquid mixtures. The ultrasonic velocities of the binary liquid mixtures of acetophenone and benzene at 303.15, 313.15 and 323.15 K over the entire range have been theoretically evaluated by using various theories and compared with experimental values.


The chemicals used were of analytical reagent grade obtained from loba chemicals. All the components were dried over anhydrous calcium chloride and fractionally distilled (Oswal and Patel, 1995). Binary solutions were prepared on percentage basis (v/v) by dissolving known volume of acetophenone in appropriate volume of benzene and measuring their masses on a Shimadzu Corporation Japan Type BL 2205 electronic balance accurate to 0.01 g. The possible uncertainty in the mole fraction was estimated to be less than ±0.0001.The densities were determined by using bicapillary pycnometer as described (Mehdihasan-Ujjan et al., 1995) and calibrated with deionised double distilled water with 0.9960x103 kg m-3 as its density at temperature 303 K. The pycnometer filled with air bubble free experimental liquids was kept in a transparent walled water bath to attain thermal equilibrium. The positions of the liquid level in the two arms were recorded with a help of travelling microscope which could read to 0.01 mm. The precision density measurements were within ±0.0003 g cm-3. Speed of sound was measured by using a variable path, single crystal interferometer (Mittal Enterprises, New Delhi). The interferometer was calibrated using toluene. The interferometer cell was filled with the test liquid and water was circulated around the measuring cell from a thermostat. The uncertainty was estimated to be 0.1 m sec-1. All measurements were made in a thermostatically controlled water bath with temperature accuracy of ±0.1°C.

Theory: Using experimentally measured values of ultrasonic velocity (u) and density (ρ) the following acoustic and thermodynamic parameters are evaluated (Subha et al., 2004; Riggio et al., 1986; Mehra and Pancholi, 2007; Mehra et al., 2001). The internal pressure for pure liquids and their binary liquid mixtures are calculated using the suryanarayana relation as given as:


where, b stands for cubic packing which is assumed to be 2 for liquids, K is dimensionless constant which is independent of temperature and nature of liquids and its value is 4.28x109, R is gas constant, T is absolute temperature and Meff is effective molecular weight Meff = X1M1 + X2M2

Excess Gibb’s free energy of activation of viscous flow for binary liquid mixtures are obtained by using following expression:




The volume fraction of pure components Φi, was calculated from the individual pure molar volumes (Vi), with the relationship:


On assuming additivity of molar sound velocity Nomoto (1958) established the following equation for sound velocity:


where, xi is the molefraction, Ri = uiVi1/3 the sound velocity, Vi the molar volume and ui is the sound velocity of the ith component. Junjie’s equation is given by:


Rao’s (specific sound velocity) relation (Gokhale and Bhagavat, 1989) is given by:


where, ri= ui1/3/ρi is the Rao’s specific sound velocity of the ith component of the mixture.


Table 1 summarizes the comparison of density (ρ) and ultrasonic velocity (u) data for pure liquids (acetophenone and benzene) at 303.15 K with the literature. The calculated quantities of internal pressure (πi), excess gibbs energy (GE), free volume (Vf) and viscous relaxation time (τ) of acetophenone and benzene system over the entire composition range at 303.15 K, 313.15 K and 323.15 K have been presented in Table 2.

Excess internal pressure (πiE), excess velocity (UE) and excess free volume (VfE) were calculated from the experimental results by the following equations, respectively:




where, X1 and X2 are mole fractions, πi1 and πi2 are the internal pressures, U1 and U2 are the velocities and Vf1 and

Table 1: Comparison of experimental density and sound of velocity of pure liquids with literature values at 303.15 K

Table 2: Experimental parameters (ρ, u), derived parameters (internal pressure, Gibb’s free energy, free volume, relaxation time) for acetophenone + benzene system at 303.15, 313.15 and 323.15 K

Vf2 are the free volumes of component 1 and 2 respectively. The subscript M represents mixture properties. The variations of πiE, UE, GE and VfE with the molefraction of acetophenone at 303.15, 313.15 and 323.15 K are presented in Fig. 1-4.

The excess values of thermo physical properties and thermo acoustical parameters of binary liquid mixtures are fitted to a Redlich-Kister (Redlich and Kister, 1948) equation of the type:


where, Y represents excess internal pressure, excess free volume the corresponding equation. Coefficients Ai were obtained by fitting equation to experimental values using a least square regression method. In each case, the optimum number of coefficients is ascertained from an examination of the variation in standard deviation (S). S was calculated using the relation:


Fig. 1: Excess Gibb’s energy of activation of flow for acetophenone (1) + benzene (2) at different temperatures

where, N represents the number of experimental data points and n is the number of coefficients. It is found that for the solution of the seventh degree polynomial, the agreement between the experimental values and the calculated values is satisfactory. The coefficients and standard deviations of Redlich-Kister polynomial equation are presented in Table 3.

Table 3: Redlich-Kister constants for excess internal pressure and excess Gibb’s free energy of Acetophenone - benzene at 303.15, 313.15 and 323.15 K

Fig. 2: Excess Velocity for acetophenone (1) + benzene (2) at different temperatures

Fig. 3: Deviation of internal pressure for acetophenone (1) + benzene (2) at different temperatures

The excess Gibb’s free energy of activation of viscous flow, ΔG*E is positive over the entire mole fraction range for the binary mixtures at different temperatures in Fig. 1. The sign of the values of ΔG*E can be considered as a reliable criterion for detecting or excluding the presence of interaction between unlike molecules. The positive ΔG*E values are also indicative of the strong molecular interaction between acetophenone and benzene. A detailed observation shows that the deviations of ultrasonic velocity of a mixture show increasing trend when mole fraction and temperature increases. It may be noted that such values are due to the electronic perturbation of the individual molecules during mixing and therefore depend very much on the nature of the mixing molecules. The internal pressure deviations are negative over the entire composition range of mixtures.

Fig. 4: Excess free volume for acetophenone (1) + benzene (2) at different temperatures

The excess free volumes are negative over the entire composition range of mixtures(Fort and Moore, 1965; Mehra et al., 2001). This suggests that the component molecules are closer together in the liquid mixture than in the pure liquids forming the mixture, indicating that strong attractive interactions between component molecules such as hydrogen bonding, dipole-dipole interactions and other specific interactions between unlike molecules are operative in the system.

The experimental and theoretical velocities calculated by using the Eq. 6-8 are presented in Table 4. The validity of different theoretical formulae is checked by percentage deviation for all the mixtures at all the temperatures and is given in Table 4. The limitations and approximation incorporated in these theories are responsible for the deviations of theoretical from experimental values. In Nomoto’s theory, no interaction between components of liquid mixtures has been taken into account as it is supposed that the volume does not change on mixing. Similarly the assumption for the formation of ideal mixing relation is that, the ratios of specific heats of ideal mixtures and the volumes are equal by not taking into the consideration of molecular interactions. Various types of forces such as dispersion forces, charge transfer, hydrogen bonding, dipole-dipole and dipole-induced dipole interactions are operative due to interactions when two liquids are mixed. This is in good agreement with the conclusions drawn by Padey et al. (1999) Thus the observed deviation of theoretical values of velocity from the experimental values shows that the molecular interactions is taking place between the unlike molecules in the liquid mixture.

Table 4: Values of ultrasonic velocity calculated from Nomoto, Junjie’s and Rao’s relations along with experimental ultrasonic velocity and percentage error for acetophenone +benzene at 303.15, 313.15 and 323.15 K

There is a good agreement between experimental and theoretical values in Nomoto’s relation followed by Rao’s specific velocity method whereas higher deviations are observed in Junjie’s relations at all the temperatures.


Experimental data of the density and speed of sound of acetophenone and benzene mixtures have been measured over the entire composition range at 303.15, 313.15 and 323.15 k. it has been observed that positive deviations for excess velocity, excess internal pressure, excess Gibbs energy where as negative deviations were observed for excess free volume at 303.15, 313.15 and 323.15 k. The observed deviation of theoretical values of velocity from the experimental values is attributed to the presence of intermolecular interactions in the systems studied. It may be concluded that out of three theories and relations, Nomoto’s relation is best suited for the binary mixture of acetophenone +benzene at 303.15, 313.15 and 323.15 k.

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